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Representation Theory

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Generic extensions and multiplicative bases of quantum groups at ${{\mathbf q=0}}$

Author: Markus Reineke
Journal: Represent. Theory 5 (2001), 147-163
MSC (2000): Primary 17B37; Secondary 16G30
Published electronically: June 12, 2001
MathSciNet review: 1835003
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Abstract: We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at $q=0$ of Ringel’s Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig’s canonical basis.

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Additional Information

Markus Reineke
Affiliation: BUGH Wuppertal, Gaußstr. 20, D-42097 Wuppertal, Germany
MR Author ID: 622884

Received by editor(s): August 14, 2000
Received by editor(s) in revised form: April 10, 2001
Published electronically: June 12, 2001
Article copyright: © Copyright 2001 American Mathematical Society